Problem: Solve for $x$ : $ 6|x + 9| + 10 = -4|x + 9| + 3 $
Explanation: Add $ {4|x + 9|} $ to both sides: $ \begin{eqnarray} 6|x + 9| + 10 &=& -4|x + 9| + 3 \\ \\ { + 4|x + 9|} && { + 4|x + 9|} \\ \\ 10|x + 9| + 10 &=& 3 \end{eqnarray} $ Subtract ${10}$ from both sides: $ \begin{eqnarray} 10|x + 9| + 10 &=& 3 \\ \\ { - 10} &=& { - 10} \\ \\ 10|x + 9| &=& -7 \end{eqnarray} $ Divide both sides by ${10}$ $ \dfrac{10|x + 9|} {{10}} = \dfrac{-7} {{10}} $ Simplify: $ |x + 9| = -\dfrac{7}{10}$ The absolute value cannot be negative. Therefore, there is no solution.